Observational Signatures of Dyonic Black Holes in Non-Linear Electrodynamics

The gist The study investigates thin-disk accretion and emission spectra for static, spherically symmetric dyonic black holes in non-linear electrodynamics (NLED), finding that modifications to NLED lead to a shrinkage of the ISCO radius, resulting in a shift of the radiation spectrum thermal maximum towards smaller radii and an increase in the local effective temperature compared to standard solutions

Theoretical Framework

The research utilizes non-linear electrodynamics (NLED) to model dyonic black holes, which carry both electric and magnetic charges simultaneously, introducing a new gravitational potential and modifying the geometry in the strong-field regime. In contrast to classical Maxwell theory, where electromagnetic duality assumes equal charges, the coupling parameters in NLED introduce a new gravitational potential and modify the geometry in the strong-field regime. The spacetime metric is specified by six parameters: mass of the black hole m, cosmological constant Λ, its charge q, magnetic charge p, and non-linear electrodynamics couplings a and b. In the purely magnetic case (q = 0), the existence of the event horizon for an arbitrary value of the mass is assured if p squared ηa with η ≈ 13.987, an extremal solution appears.

Geodesic Motion and Accretion Disk Kinematics

The study derives the equations of motion and the effective potential to evaluate the system’s dynamics, considering a Lagrangian L for a point particle around the dyonic black hole in non-linear electrodynamics. The dimensionless quantities are defined by scaling with appropriate powers of the black hole mass m, allowing computations to be performed with m = 1 without any loss of generality. The effective potential is given by Vef f = f(r) / (1 + L squared r 2). The dimensionless radius of the innermost stable circular geodesic orbit is obtained from d 2V¯eff dr¯ 2 = 0.

Thin Accretion Disk Signatures

The kinematic parameters for particles in circular orbits, such as their angular velocity, specific energy, and specific angular momentum, are calculated using dimensionless quantities. The angular velocity increases as particles move toward the black holes, reaching high values near the event horizons. The specific energy E¯ exhibits three phases: far from the black hole, near the black hole, and close to the event horizon. The specific angular momentum L¯ is very similar to the specific energy for all cases.

Observational Signatures and EHT Constraints

The study examines several key observational signatures, including the continuum thermal spectrum, radiative efficiency, the photon sphere radius, and the black hole shadow. The NLED correction to the gravitational potential changes the innermost stable circular orbit (ISCO), which affects the disk temperature, spectrum, and radiative efficiency. The thermal peak moves to smaller radial positions and greatly increases its value compared to the Schwarzschild vacuum background due to the closer proximity of ISCOs. The black hole shadow radius is defined by the unstable photon orbits, and for NLED spacetimes, these shadows show clear deviations from the Schwarzschild and RN metrics. The goodness of fit test using the angular diameter constraints at the horizon scale collected by the Event Horizon Telescope (EHT) concerning Sagittarius A∗ (Sgr A∗) proves that both these dyonic NLED and purely magnetic models have good statistical agreement with experimental data.

Conclusion

The study concludes that the thin accretion disk around dyonic and purely magnetic NLED black holes displays distinct observational signatures that could be used in future observations. The modified gravitational potential allows us to detect changes in the ISCO radius, thermal spectrum, radiative efficiency, photon sphere, and black hole shadow. The good agreement between the considered NLED models and EHT observations of Sgr A∗ confirms the viability of the non-linear electrodynamics framework for describing the strong-field regime of black holes.

How it works

The analysis involves several steps to characterize these complex systems. First, the metric function f(r) is determined by numerically solving a cubic equation for Frt(r) at each radial step. Second, the geodesic equations of motion are obtained using conserved quantities E and L in the equatorial plane. Third, the effective potential Vef f is derived from these equations to describe test particle dynamics. Finally, for astrophysical applications, the radiation behavior is calculated using the relation F(r) = −M˙0 / (4π√−g¯omega¯r)(E¯ − omega¯L¯)2Z r/rISCO(E¯ − omega¯L¯)L̄rdr.

Key Findings

The research established several key findings regarding the effects of NLED on black hole properties. The modifications to NLED lead to a shrinkage of the ISCO radius, which consequently shifts the radiation spectrum thermal maximum towards smaller radii and an increase in local effective temperature. The presence of electric and magnetic charges causes the thermal peak to move to smaller radial positions and greatly increase its value compared to the Schwarzschild vacuum solution. Furthermore, the ISCO radius moves inward as charge parameters increase, which has a strong impact on accretion disk physics. The shadow contours for different black holes in this case show clear deviations from the Schwarzschild and RN metrics, especially when coupling constants of the NLED black holes (a, b) and the cosmological constant Λ are high.

Observational Validation

The comparison of theoretical shadow angular diameters with EHT observations of Sagittarius A∗ (Sgr A∗) is a crucial test. The models for which χ2 < 1 indicate excellent agreement within the 1σ experimental error, and the best model is the one with parameters (a, b, q, p,Λ) at θ = 48.7 µas. The overall matching presented in Fig. (32) shows that non-linear magnetic fields demonstrate high statistical compatibility with current measurements of the horizon.

Summary of Results

The work systematically investigated the observational signatures of static, spherically symmetric dyonic black holes in non-linear electrodynamics, focusing on thin accretion disk properties and the resulting electromagnetic radiation. The primary objective was to understand how the modifications to the gravitational potential arising from the NLED framework manifest in astrophysical observables that can be tested against current and future observations. The results prove that the thin accretion disk around dyonic and purely magnetic NLED black holes displays distinct observational signatures that could be used in future observations.

How it works

The investigation proceeds by considering the most general metric of a dyonic black hole extracted from the NLED action, depending on six parameters: mass, cosmological constant, electric and magnetic charge, and NLED coupling constants. Due to the complexity of the problem, the electrostatic field Frt depends on a third-degree polynomial and could be analytically solved only for the case q = 0. In this case, we obtained an analytical solution that shows the most important modification of the metric function f(r) due to the 1/r 6 term. The most intriguing fact about this term is the increase of its contribution with the distance to the event horizon; therefore, it will make essential contributions to the deviation of the black hole solution from the standard Schwarzschild or Reissner-Nordstr¨om cases.

Key Findings

The study established several key findings regarding the effects of NLED on black hole properties.

1. Bold header: Improved Astrophysical Parameter Estimation

This system can now perform a goodness-of-fit test through the angular diameter constraints at the horizon scale collected by the Event Horizon Telescope (EHT) using Equation (39) to statistically compare theoretical models against observational data, as demonstrated in Fig. 25 and Table V.

2. Bold header: Enhanced Spectral Modeling for X-ray Signatures

The improved system can calculate the continuum thermal spectrum and effective temperature using Stefan-Bolt by integrating blackbody radiation over stable annular regions starting from the ISCO, directly linking NLED modifications to observable spectral features as shown in Fig. 21 and Table III.

3. Bold header: Robust Black Hole Shadow Contouring

The system can numerically calculate the photon sphere radius (Equation 34) and black hole shadow radius is defined by the unstable photon orbits to generate precise shadow contours, allowing for direct comparison with EHT measurements, as illustrated in Fig. 24 and Table IV.

4. Bold header: Quantifiable Constraints on NLED Couplings

The system can use the statistical distribution of the goodness-of-fit test (the chi-squared value) to put restrictions on the NLED coupling constants a and b, providing empirical bounds for theoretical extensions based on current EHT constraints.

We study the observational features of thin-disk accretion and emission spectra for static, spherically symmetric dyonic black holes in non-linear electrodynamics (NLED). In contrast to classical Maxwell theory, where electromagnetic duality assumes equal charges, the coupling parameters in NLED introduce a new gravitational potential and modify the geometry in the strong-field regime. We also study the kinematic characteristics of particles on circular orbits, such as their angular velocity, specific energy, and specific angular momentum. It is found that modifications of NLED lead to a shrinkage of the ISCO radius, resulting in a shift of the radiation spectrum thermal maximum towards smaller radii and, consequently, an increase in the local effective temperature in comparison with the standard Schwarzschild and Reissner-Nordström solutions. Additionally, we compute null-geodesic orbits to determine the optical edge of both the photon sphere and the black hole shadow. In order to assess the observational validity of the aforementioned alternatives, we carry out a χ squared goodness-of-fit test through the angular diameter constraints at the horizon scale collected by the Event Horizon Telescope (EHT) concerning Sagittarius A* (Sgr A*). We prove that both these dyonic NLED and purely magnetic models have good statistical agreement with experimental data.